Explicație pas cu pas:
d)
[tex] |x + 3| < 5 \\ - 5 < x + 3 < 5 \\ - 8 < x < 5 \\[/tex]
[tex]x \in \mathbb{Z} = > A = \{ -7; -6; -5; - 4; - 3; - 2; - 1; 0; 1; 2; 3; 4 \} \\ [/tex]
[tex] |x| \leqslant 7 \\ - 7 \leqslant x \leqslant 7[/tex]
[tex]x \in \mathbb{Z} = > B = \{ -7; -6; -5; - 4; - 3; - 2; - 1; 0; 1; 2; 3; 4; 5; 6; 7 \} \\ [/tex]
e)
[tex]4x + 11 > 67 \\ 4x > 67 - 11 \\ 4x > 56 \\ x > 56 \div 4 \\ = > x > 14[/tex]
[tex]x \in \mathbb{N} = > A = \{15; 16; 17; 18... \} \\[/tex]
[tex]7x - 5 \geqslant 72 \\ 7x \geqslant 72 + 5 \\ 7x \geqslant 77 \\ x \geqslant 77 \div 7 \\ x \geqslant 11[/tex]
[tex]x \in \mathbb{N} = > B = \{11; 12; 13; 14; ... \} \\[/tex]
f)
[tex]( {x}^{2} - 3) \: | \: 22 \\ x \in \mathbb{N} = >( {x}^{2} - 3) \in \{1;2;11;22\} \\ {x}^{2} \in \{4;5;14;25\} = > A = \{2;5\}[/tex]
[tex] |x| \leqslant 5 \\ - 5 \leqslant x \leqslant 5[/tex]
[tex]x \in \mathbb{Z} = > B = \{-5; - 4; - 3; - 2; - 1; 0; 1; 2; 3; 4; 5 \} \\ [/tex]
